1. Field of the Invention
The present invention relates to an information processing apparatus that numerically analyzes an incompressible fluid and a method therefor.
2. Description of the Related Art
An equation of motion that describes an incompressible fluid includes a term (pressure term) indicating that a fluid is accelerated by a pressure, and a term (advective term) indicating that a momentum is conveyed such that the fluid itself flows.
Regarding pressure, methods that numerically analyze incompressible fluids include two typical methods, one using calculus of finite differences and the other one using a finite element method (see “Nagare-no Suchi Shimyureshon (Numerical Simulation of Fluid)”, Japan Society of Mechanical Engineers, Corona Publishing Co., Ltd.). To use the calculus of finite differences (central difference for pressure), a method, called a “staggered mesh technique”, of placing physical quantities is commonly used.
In the staggered mesh technique, a spatial component of the momentum of a fluid and its pressure are all placed at different points. When the staggered mesh technique is not used, a contrivance, such as raising the accuracy of spatial differentiation of pressure, is needed. If such a contrivance is not performed, nonphysical vibration occurs in a pressure field. Although, in the finite element method, a definition point of a momentum vector and a definition point of pressure can be placed at the same point, when a pressure Poissson's equation concerning an incompressible fluid is solved, it is necessary to increase the order of an interpolation function of a velocity field rather than increasing the order of an interpolation function of pressure. In addition, the finite element method has a numerical calculation load larger than that of the calculus of finite differences.
Regarding the advective term, a case in which the definition points of physical quantities are placed at the same point is less complicated as a method.